Abstract

We study the displacement flow of two Newtonian fluids in an inclined pipe. The fluids have the same viscosity but different densities. The displacing fluid is denser than the displaced fluid and is placed above the displaced fluid (i.e., a density-unstable configuration). Three dimensionless groups describe these flows: a densimetric Froude number Fr, a Reynolds numberRe, and the pipe inclination β. Our experiments cover fairly broad ranges of these parameters: 0 ⩽ Fr ⩽ 9; 0 ⩽ Re ⪅ 2400; 0 ⩽ β ⩽ 85°. Phenomenologically, our experimental flow observations vary from well mixed fully diffusive regimes, through buoyancy-dominated inertial exchange regimes, to laminar viscousflows, all with varying degrees of stability. We characterize the different flow regimes observed in terms of the three dimensionless groups and provide leading order approximations to the velocity of the displacement front and the macroscopic diffusion in each regime.

Received 18 December 2012Accepted 04 April 2013Published online 11 June 2013

Acknowledgments:

This research has been carried out at the University of British Columbia, supported financially by NSERC and Schlumberger through CRD project 354716-07. The authors also thank Messrs. Ethan Stuart, Hady Abou Jaoude, and George Hatzikiriakos for assisting in running the experiments. We thank the reviewers for helpful comments.